Five days after the Navy disclosed widespread cheating on nuclear tests by schoolhouse instructors, the Navy’s top officer reemphasized the importance of personal integrity and stressed that discussions of what it means should not be limited to boot camp or ROTC units.

“I don’t think we have an ethics problem across the Navy,” Chief of Naval Operations Adm. Jon Greenert said in one of three one-minute videos posted Sunday. “But I think we need to reinforce our core values and our core commitment to honor, courage and commitment.

“Integrity is the foundation of what we’re about,” Greenert continued. “We need to talk about that — that has to be part of our training program. I’m not just talking about General Military Training. We need to talk about it in the ready rooms, we need to talk about it on the bridge of our ships, we need to talk about it on our squadron flight lines, in the hangar bay and in our bilges — and we need to commit to it full-time.”

The Navy has said that 30 “senior sailors” at the Nuclear Power Training Unit in Charleston, S.C., have been implicated in cheating on standard exams that would qualify them to operate nuclear reactors, like the one at NPTU. Officials said that one-fifth of all the engineering watch supervisors at Nuclear Power School have had their access to the school pulled; if found guilty, they will be stripped of their nuclear certifications and likely kicked out of the service.

It is the Navy’s first nuclear cheating scandal in three years, coming on the heels of more troubling allegations among Air Force officers who oversee the nation’s intercontinental ballistic missiles. Unlike those cases, the Navy ring happened in a schoolhouse.

The Pentagon — whose leadership believes rooting out these problems is a top priority — has launched wide-ranging reviews of the military’s nuclear enterprise. One review is focusing on the personnel policies and training for those who secure the Navy’s nuclear weapons, like Trident ballistic missiles launched from Ohio-class submarines. The reviews will also assess the service’s ethos to determine whether some of these issues may be systemic.

“We’re going to look at our values, at our integrity, at our character and make sure we’re not talking past each other,” Greenert said. “That we’re actually talking with each other to understand the foundation of integrity.”